Stanley twice halved a two-goal deficit in the second half, but Matt Grimes scored the decisive goal as the visitors record a fifth away success of the season.
The Grecians came from two down to beat Shrewsbury Town last Saturday, but they opened the scoring this evening as Liam Sercombe netted on the stroke of the break.
The midfielder finished powerfully from inside the box to give Exeter a slender advantage at the end of a first half in which injured referee Andy Haines had to be replaced by fourth official Ricky Wooton.
Paul Tisdale's side doubled their lead four minutes into the second period as Tom Nichols capitalised on space afforded to him on the edge of the box to emphatically strike his sixth goal in five league games.
Accrington pulled one back when John O'Sullivan found the top corner from range, but City restored their cushion moments later when Grimes produced the pick of five impressive goals on the night with a 30-yard free kick which flew beyond on-loan keeper Jack Rose on 69 minutes.
There was still fight in the hosts, though, and substitute Shay McCartan brought them within one again when he guided the ball into the bottom corner after making a run from deep to meet Andrew Proctor's cross.
McCartan struck over the crossbar from 20 yards, while Rob Atkinson glanced a header just wide in the closing stages as Exeter hung on for three points which take them to within a place of the playoff spots.